CHARLESTON, South Carolina (CNN) -- Responding to critics who say that al Qaeda in Iraq is not the same group that attacked the United States on Sept. 11, 2001, President Bush on Tuesday shared intelligence information he said links the two.

President Bush said Tuesday that al Qaeda in Iraq is part of Osama bin Laden's terrorist network.

Charges that al Qaeda in Iraq did not exist until the U.S. "invasion of Iraq and that it's a problem of our own making" are part of the "flawed logic that terror is caused by American actions," Bush said.

"Al Qaeda in Iraq is run by foreign leaders loyal to Osama bin Laden," Bush said. "Like bin Laden, they are cold-blooded killers who murder the innocent to achieve al Qaeda's political objectives.

"Yet, despite all of the evidence, some will tell you that al Qaeda in Iraq is not really al Qaeda and not really a threat to America."

At least one intelligence analyst suggested a focus on al Qaeda in Iraq oversimplifies the problem there. Former acting CIA director and CNN national security adviser John McLaughlin said the situation is more complex.

"No question al Qaeda in Iraq is an important part of this conflict," McLaughlin said. "But to describe it in just those terms is to describe really a game of checkers when what we're dealing with here is a game of chess. Because we have many other facets to this conflict, including a civil war, including tensions between tribes, nationalists and so forth."

CNN's Michael Ware, who is based in Baghdad, said the fact that al Qaeda in Iraq is part of the broader terror network has never been in question. He called Bush's speech "an ancient history lesson."

"It makes one wonder why the president is hammering this point home when he glosses over the fact this war is creating more al Qaeda jihadis rather than reducing their number," Ware told CNN's Wolf Blitzer. Watch Ware's take on the president's speech »

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Bush's comments at Charleston Air Force Base came one day after eight Democratic presidential hopefuls debated at the state's famed Citadel military college. Several of them had harsh words for the president's handling of the Iraq war and his justifications for it.

Critics of the war have complained about the Bush administration's insistence that Iraq is the central front in the war on terrorism, saying the war has been a recruiting tool for terrorists.

They say that the administration has dropped the ball in Afghanistan, where a resurgent Taliban is fighting to regain control, and Pakistan, where both the Taliban and al Qaeda have based their efforts to regroup.

Sen. John Kerry, D-Massachusetts, took issue with the president's speech, saying he was "trying to scare the American people."

"We all understand al Qaeda is a danger, and we all understand what its goals are, but 9/11 was not plotted in Iraq," he said, citing the recent National Intelligence Estimate that the terror group had reconstituted itself in Pakistan and that the invasion of Iraq had attracted forces to al Qaeda.

Kerry said that al Qaeda is "not the principal killer of American forces" in Iraq and that a home-grown insurgency and Shia and Sunni militants are more of a danger.

Many critics, particularly among the Democrats, want a timeline to bring U.S. troops back from Iraq and perhaps redeploy them in Afghanistan.

Tuesday, Bush attempted to take aim at those critics, mentioning al Qaeda 93 times in the 29-minute speech in an attempt to convince Americans that U.S. troops must stay in Iraq. The strategy is a simple one -- emphasize al Qaeda's role in the violence rather than the fighting between warring Iraqi groups.

The enemy now in Iraq, Bush argued, is the same enemy that attacked the United States on Sept. 11, 2001.

Citing what he called "newly declassified information," Bush said that the founder of al Qaeda in Iraq, Jordanian-born Abu Musab al-Zarqawi, ran a terrorist training camp in Afghanistan and had long-standing relations with senior al Qaeda leaders bin Laden and his top deputy, Ayman al-Zawahiri.

In 2001, Bush said, al-Zarqawi fled Afghanistan after his training camp was bombed by U.S. forces and went to Iraq, where he created the Unification and Jihad group.

The group was accused in the beheading deaths of several Western hostages, including Nicholas Berg, and in dozens of brutal suicide attacks that killed Iraqi citizens and U.S. troops.

It was in 2004, Bush said, that al-Zarqawi declared his allegiance to bin Laden, and the central al Qaeda leader anointed al-Zarqawi the prince of al Qaeda in Iraq, directing followers to obey him.

"The merger between al Qaeda and its Iraqi affiliate is an alliance of killers," Bush said.

When al-Zarqawi was killed in a U.S. airstrike in 2006, he was replaced at the helm of al Qaeda in Iraq by Egyptian-born Abu Ayyub al-Masri.

U.S. intelligence information shows that al-Masri taught in Afghanistan and had ties with al-Zawahiri for nearly 20 years, the president explained.

Bin Laden sent a trusted adviser, Abd al-Hadi al-Iraqi, to Iraq to help al-Masri, Bush said, but the man was captured en route and sent to Guantanamo Bay Naval Base, where hundreds of suspected terrorists are being held.

"The fact that Osama bin Laden risked sending one of his most valuable commanders to Iraq shows the importance he places on success of al Qaeda's Iraqi operations," the president said.

Bush also listed several other non-Iraqi leaders of al Qaeda in Iraq, confirming, he said, "our intelligence that foreigners are the top echelons of al Qaeda in Iraq and that the foreign leaders make most of the operational decisions, not Iraqis."

"Al Qaeda in Iraq is a group founded by foreign terrorists, led large by foreign terrorists and loyal to a foreign terrorist leader, Osama bin Laden," the president said. "They know they're al Qaeda. The Iraqi people know they are al Qaeda. People across the Muslim world know they are al Qaeda.

"And there's a good reason they are called al Qaeda in Iraq. They are al Qaeda. In Iraq."

U.S. intelligence considers al Qaeda in Iraq part of al Qaeda's "decentralized chain of command, not a separate group," the president said. "They are a full member of the al Qaeda terrorist network."

Bush said those in Washington who make a distinction between the two groups are trying to paint the war in Iraq "as a distraction from the real war on terror."

"If we're not fighting bin Laden's al Qaeda, they can argue that our nation can pull out of Iraq and not undermine our efforts in the war on terror," he said.

"The problem they have is with the facts. We are fighting bin Laden's al Qaeda in Iraq; Iraq is central to the war on terror; and against this enemy, America can accept nothing less than complete victory."E-mail to a friend

CNN White House Correspondent Suzanne Malveaux contributed to this report.